university of illinois frederick seitz materials research laboratory dislocation-driven surface...

University of Illinois Frederick Seitz Materials Research Laboratory

Dislocation-DrivenDislocation-DrivenSurface Dynamics on SolidsSurface Dynamics on Solids

Sanjay V. KhareSanjay V. Khare11, Suneel Kodambaka,, Suneel Kodambaka,Wacek Swiech,Wacek Swiech, Kenji Ohmori, Ivan Petrov,Kenji Ohmori, Ivan Petrov, & Joe Greene& Joe Greene

Dept. of Materials Science and Frederick Seitz Materials Research Laboratory

University of Illinois at Urbana-Champaign

Funded by US-DOE through grant DEFG02-91ER45439

Frederick Seitz Materials Research

Laboratory

11Department of Physics and Astronomy University of Toledo


Dislocations in solidsBulk dislocation dynamics have been extensively studied.

Surface-terminated dislocations affect nanostructural and interfacial stability, crystal growth kinetics, mechanical, chemical, & electronic properties of solids.

Bulk dislocation dynamics have been extensively studied.

Surface-terminated dislocations affect nanostructural and interfacial stability, crystal growth kinetics, mechanical, chemical, & electronic properties of solids.

Very little is known concerning the effects of dislocations on surface dynamics.

250 Å

Brune, Giovannini, Bromann, & K. Kern

Nature 394, 451 (1998)

Teng, Dove, Orme, & J.J. De Yoreo

Science 282, 724 (1998)

Spila, Desjardins, D’Arcy-Gall, Twesten, & J.E. Greene,

JAP 93, 1918 (2003)

SiGe/Si Ag/Pt KDP


*K.F. McCarty & N.C. Bartelt: Phys. Rev. Lett. 90, 046104 (2003);Surf. Sci. 527, L203 (2003);Surf. Sci. 540, 157 (2003);Journal of Crystal Growth 270, 691 (2004).

Develop fundamental understanding of the effect of dislocations on surface dynamics

Model system: TiN

Use LEEM to investigate surface morphological evolution kinetics as a function of:

annealing timetemperature &N2 partial pressure.*

Objectives


S. Kodambaka, N. Israeli, J. Bareño, W. Święch, K. Ohmori, I. Petrov, & J.E. Greene, Surf. Sci. 560, 53 (2004).

2D TiN(111) island decay:detachment-limited

kinetics+

highly permeable steps

2Np = 5x10-8 TorrT = 1550 K

2.8±0.3 eV2.8±0.3 eV

7.0 7.2 7.4104

105

T (K)

dA

/dt

(Å2 /s

)

1/kT (eV -1

)

1640 1600 1560

TiN/TiN(111)


TiN/TiN(111) Spirals

field of view: 2.5 m

treal = 90 s tmovie = 9 s

T = 1688 K ~ 0.5Tm

2Np = 5x10-8 Torr

Observed during annealing in the absence of deposition/evaporation NOT BCF spirals


• near-equilibrium*• shape-preserving• periodic• absenceabsence of applied applied

stressstress & net mass net mass change by change by deposition/evaporation.deposition/evaporation.

t = 0 s 15 s

31 s 47 s

*S. Kodambaka, V. Petrova, S.V. Khare, D.D. Johnson, I. Petrov, & J.E. Greene, Phys. Rev. Lett. 88, 146101 (2002).

= 47 s= 47 s

TiN(111) spiral step growthT = 1688 K


TiN/TiN(111)

2Np = 5x10-8 Torr

field of view 5.6 m


Spirals grow with a constant & 2D island areas decrease at a constant rate

T = 1670 K

2

4

6

t (

rad

ian

s)

0 60 120 180 240

4

8

12

A (

10-2

m2 )

t (s)

2

4

6

t (

rad

ian

s)

0 60 120 180 240

4

8

12

A (

10-2

m2 )

t (s)

SpiralSpiral

0 10 20 30 40

0.00

0.02

0.04

0 30 60 90

0.8

1.0

1.2

A (m

2 )

Island

t (s)

T = 1690 K


1

10

(1

0-2 r

ad/s

)

1720 1680 1640 1600

T (K)

103

104

dA

/dt/

(1/s

)

TiN(111) spirals:TiN(111) spirals:

EEgrowthgrowth = 4.6±0.2 eV = 4.6±0.2 eV

C = 10C = 1012.6±0.612.6±0.6 s s-1-1

2D TiN(111) islands*:2D TiN(111) islands*:

EEdecaydecay = 3.1±0.2 eV = 3.1±0.2 eV

C = 10C = 1013.6±0.613.6±0.6 s s-1-1

2Np = 5x10-8 Torr

TiN/TiN(111)

*S. Kodambaka, N. Israeli, J. Bareño, W. Święch, K. Ohmori,

I. Petrov, & J.E. Greene, Surf. Sci. 560, 53 (2004).

TiN(111) spiral step kinetics is different from that of 2D islands.


TiN/TiN(111)

2D island decay: E2D island decay: Eaa = 2.8 eV = 2.8 eV

Spiral step growth: ESpiral step growth: Edd = 4.6 eV = 4.6 eV

Ti or TiN desorption*: ETi or TiN desorption*: Eevaporationevaporation ~ 8-10 eV ~ 8-10 eV

Ea << Ed << Eevaporation*D. Gall, S. Kodambaka, M.A. Wall, I. Petrov, & J.E. Greene,

J. Appl. Phys. 93, 9086 (2003).

Spiral nucleation and growth MUST be due to bulk mass transport !!

Proposed mechanism:• driving force: bulk dislocation line energy minimization

surface spiral step formation via bulk point defect transport• dislocation cores emit/absorb point defects at a constant thermally-

activated rate.S. Kodambaka, S.V. Khare, W. Święch, K. Ohmori, I. Petrov, & J.E. Greene, Nature 429, 49 (2004).

Modeling dislocation-driven spiral growth



At steady state: 2iC (r) 0

eqloop l

core

ooploop

core

s

s

r

r r

r

R

2πD C(r)

k [C

r

(r )-C ]

B.C.s:

R(T) - thermally-activated point defect emission/absorption rate

C - point defect concentration (1/Å2)

Ds - surface diffusivity (Å2/s)ks - attachment/detachment rate

(Å/s) - area/TiN (Å2)

Step velocity:

eqloop lo

loop

op

loops

dr 1Ω RΩk [C(r ) -

dC =

π r]

2t

constant growth rate dA/dtconstant growth rate dA/dt

rcore

rloop

S. Kodambaka, S.V. Khare, W. Święch, K. Ohmori, I. Petrov, & J.E. Greene, Nature 429, 49 (2004).


is a thermally-activated is a thermally-activated constantconstantAo : area outside of which R is

negligible : area/TiN (Å2) : spiral angular velocity (rad/s)R(T) : thermally-activated point defect

emission/absorption rate

o

2R

A

Total surface flux = R/Ao

1 rotation 1 ML in 2/ sec



1 m0 4 8 12

7

8

9

(1

0-2 r

ad/s

)

t (102 s)

decreases monotonically with annealing time

field of view 5.6 m

T = 1725 K

2Np = 5x10-8 Torr

d/dt ~ 10-5 1/s2 at 1725 K

TiN/TiN(111) vs. t


2D TiN(111) island & spiral step kinetics are independent of N2 partial pressure

3.0

3.2

3.4

3.6

3.8

(1

0-2 r

ad/s

)

5x105x10-8-8 5x105x10-7-7

0 5 10 15 209

10

11

12

dA

/dt

(10-4

m

2 /s)

t (102 s)

vacuum

2NP (Torr)5x105x10-7-7

vacu

um

5x105x10-8-8 Torr Torr5x105x10-7-7 Torr Torr

vacuum vacuum (< 5x10(< 5x10-9 -9 TorrTorr))

1 m

T = 1670 K

TiN/TiN(111) vs. pN2


Espiral is independent of N2 pressure & sample history

6 .8 7 .0 7 .2

0 .01

0 .1

(rad

/s)

1 /kT (1 /eV )

1720 1680 1640T (K )

4.5±0.4 eV4.5±0.4 eVat 5x10-8 Torr

4.6±0.2 eV4.6±0.2 eVin vacuum

TiN/TiN(111)


• Investigated the nucleation & growth kinetics of TiN(111) spiral steps using HT-LEEM.

• Spiral growth is qualitatively & quantitatively different from 2D island coarsening/decay.

• Spiral growth is localized BCF growth/etch spirals.

• Angular velocity:* decreases with time irrespective of N2 pressure.

* does not vary significantly with spiral geometry.

* thermally-activated with a constant energy barrier (~ 4.5 eV), independent of the sample history & N2 pressure.

Conclusions


LEEM – Modes of Operation

Bright Field LEEM Dark Field LEEM

Photoemission (PEEM) Mirror microscopy (MEM)


2D TiN(111) island decay

ALL islands in the cone decay at nearly same rates

mass is not conserved locally

0 2 4 6 8

0.1

0.2

0.3

0.4

A

(m

2 )

0 1 2 3 4 5

0.2

0.4

0.6

0.8

1.0

A (m

2 )

ta (102 s)

0 2 4 6

0.1

0.2

0.3

0.4

0 2 4 6

0.1

0.2

0.3

ta (102 s)

T = 1285 oC T = 1320 oC

T = 1350 oC T = 1380 oC


Modeling decay kinetics of islands in a cone

N. Israeli and D. Kandel, PRB 60, 5946 (1999).

r1

r2

r3

Fitting variables:

Surface diffusivitySurface diffusivity D Dss

Attachment/detachment rate KAttachment/detachment rate Kdd

Step permeabilityStep permeability p pRate of bulk transportRate of bulk transport K Kbulkbulk

Step-step interaction Step-step interaction g g

• Solve 2D steady-state diffusion eqn.:

• B.C.s: adatom fluxes at island step edges

• Derive general relation for dAi/dt

• Compare calculated r vs. t with expt.l data

2i (r) 0


2D TiN island dynamics studies

2D island coarsening kinetics2D island coarsening kinetics(Ostwald ripening)(Ostwald ripening)

2D island coarsening kinetics2D island coarsening kinetics(Ostwald ripening)(Ostwald ripening)

Ta

ta

Surf. Sci. 526, 85 (2003).

Island shape Island shape fluctuation fluctuation

analysisanalysisPRL 88, 146101 (2002).

Equilibrium island Equilibrium island shapeshape

0

20

40

60

80

100

120

140

R110

R 100

100110

Surf. Sci. 513, 468 (2002).

2D island coalescence 2D island coalescence kineticskinetics

50 Å

Surf. Sci. 540, L611 (2003).


0 1 2 3 4 5

8

16

24

32

0 1 2 3 4 5

8

16

24

32

Kbulk/Kd = 2.5 &

p = 0

p/Kd = 2000 & Kbulk = 0

High g, p = 0 & Kbulk =

0

TiN/TiN(111)

T = 1350 oC o LEEM data calculation

2D TiN(111) islands decay

kinetics

detachment-limited+

highly permeable steps OR

bulk diffusion

0 1 2 3 4 5

8

16

24

32

r i (10

-2 Å

)

ta (10

-2 s)


TiN/TiN(111)

T = 1670 K

2Np = 5x10-8 Torr

field of view 5.6 m


2

4

6

t (radians)

0 60 120 180 240

4

8

12

A (

10-2

m2 )

t (s)

Spirals grow with a constant &

2D island areas decrease at a constant rate


1 m

TiN/TiN(111) vs. spiral geometry

field of view 5.6 m

2.10

2.16

2.22

0 5 10 151.35

1.38

1.41

t (102 s)

(

10-2 r

ad/s

)

2NP (Torr)

5x105x10-8-8 1010-7-71010-8-8< 10< 10-9-9

Spiral step velocities do not vary significantly with local environment

1650 K

1675 K

university of illinois frederick seitz materials research laboratory dislocation-driven surface...

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